Browsing by Subject "positive-definite kernels"

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Access status: Open Access ,
Conditional mean embedding and optimal feature selection via positive definite kernels
(Wydawnictwa AGH, 2024) Jørgensen, Palle E.T.; Song, Myung-Sin; Tian, James
Motivated by applications, we consider new operator-theoretic approaches to conditional mean embedding (CME). Our present results combine a spectral analysis-based optimization scheme with the use of kernels, stochastic processes, and constructive learning algorithms. For initially given non-linear data, we consider optimization-based feature selections. This entails the use of convex sets of kernels in a construction o foptimal feature selection via regression algorithms from learning models. Thus, with initial inputs of training data (for a suitable learning algorithm), each choice of a kernel $K$ in turn yields a variety of Hilbert spaces and realizations of features. A novel aspect of our work is the inclusion of a secondary optimization process over a specified convex set of positive definite kernels, resulting in the determination of »optimal« feature representations.